Nothing compels a stranger to give unsolicited advice like the sight of a pregnant woman. Usually, the advice revolves around eating, drinking or sleeping. “Sleep now because once the baby’s here, you won’t!” Ah, thanks for that amazing tip, random lady on the train.

But as annoying as that comment was, she had a point. In the weeks after Baby V’s birth, I was both astounded and horrified by just how little sleep our family survived on. The haze of time and extreme sleep deprivation make it hard to put numbers to the horror, but I’d guess that most days, we were lucky to get a solid 3-hour stretch. I was exhausted in a way that I didn’t know was possible.

Fortunately, the situation wasn’t permanent. Eventually babies mature enough to know day from night and begin sleeping in longer stretches. But as a new study in PLOS ONE finds, and pretty much every new parent can attest, excessive daytime sleepiness after the birth of a baby can last for months.

By combing through detailed sleep diaries of 33 women who had recently given birth, Ashleigh Filtness of Queensland University of Technology in Australia found that over half were still excessively sleepy during the day a full 4.5 months after their baby was born.

The problem wasn’t that the women weren’t getting enough total sleep. On average, they were pulling down about seven hours and 20 minutes of sleep a night. The trouble was that this sleep didn’t happen in a single, beautiful block of nighttime bliss. Night wakings splintered these women’s sleep into shards.

The women kept detailed sleep logs in the sixth, twelfth and eighteenth weeks after their baby’s birth. (The researchers believed that to ask for logs in the immediate weeks following birth would be unethical.) As time went by, sleep did improve, the logs showed. A measure called the sleep disturbance index, which is time spent awake after first going to bed relative to the total sleep time, lessened as the weeks progressed.

That’s progress. But at 18 weeks, over half of the women still reported excessive daytime sleepiness, identified by a score of 12 or higher on the Epworth Sleepiness Scale, the researchers found. In addition to being unpleasant, this pernicious drowsiness might become dangerous if, say, a new mother has to drive every day for her job.

The authors write that their study might be useful in crafting leave policies for parents. In Australia, parents are entitled to 18 weeks of paid leave after the birth or adoption of a child. And in fact, only five of the women in the study were working full time by week 18. Because there’s no magic trick to make babies sleep better, the next best thing might be to allow parents to be sleepy in the safety of their own home.